Thanks for all the tips about the tags (and how to see them in other games) and screenshots and devlogs! I went thru the tags again, and now have the full allowed 10 tags, and I also added screenshots and even video and I'll keep on making devlogs when I update the game.
I also tested and changed the Title to "HEXvolver | A Match-4 Spinning Hex Puzzle" and it immediately showed up on the search when I search for "hex puzzle". I'm pretty sure someone who comes to itch.io and uses the search "wrong", not knowing any better on how it works (just like me), might search for something like that. And I mean, on the off chance, 1 event in 10 years, I'd hate that someone would search for that and didn't see my game (which they _might_ enjoy) on the list even as the last one. Oh and just to clarify, it was never about getting my game higher up on the search for "hex puzzle", it was about _showing up_ at all.
Now the last question remains, is this kosher for itch.io? I've seen other games use descriptive words in their titles too, so if it's not, it's not at least enforced? I'll leave it like that for now as I _think_ it's okay (tried to read the docs and guidelines and quality stuff, and didn't see anything about it), and no-one here objected to it _specifically_...
Anyhoo, thanks again for the help!